# Austin L BuchananOklahoma State University - Stillwater | Oklahoma State · School of Industrial Engineering and Management

Austin L Buchanan

PhD, Industrial and Systems Engineering

## About

20

Publications

5,588

Reads

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247

Citations

Citations since 2016

Introduction

For more info, see my website:
https://austinlbuchanan.github.io/

## Publications

Publications (20)

Cliques and their generalizations are frequently used to model “tightly knit” clusters in graphs and identifying such clusters is a popular technique used in graph-based data mining. One such model is the s-club, which is a vertex subset that induces a subgraph of diameter at most s. This model has found use in a variety of fields because low-diame...

When constructing political districting plans, prominent criteria include population balance, contiguity, and compactness. The compactness of a districting plan, which is often judged by the “eyeball test”, has been quantified in many ways, e.g., Length-Width, Polsby-Popper, and Moment-of-Inertia. This paper considers the number of cut edges, which...

In critical node problems, the task is to identify a small subset of so-called critical nodes whose deletion maximally degrades a network’s “connectivity” (however that is measured). Problems of this type have been widely studied, for example, for limiting the spread of infectious diseases. However, existing approaches for solving them have typical...

Beginning in the 1960s, techniques from operations research began to be used to generate political districting plans. A classical example is the integer programming model of Hess et al. (Operations Research 13(6):998--1006, 1965). Due to the model's compactness-seeking objective, it tends to generate contiguous or nearly-contiguous districts, altho...

The usual integer programming formulation for the maximum clique problem has several undesirable properties, including a weak LP relaxation, a quadratic number of constraints and nonzeros when applied to sparse graphs, and poor guarantees on the number of branch-and-bound nodes needed to solve it. With this as motivation, we propose new mixed integ...

Cliques and their generalizations are frequently used to model ``tightly knit'' clusters in graphs, and identifying such clusters is a popular technique used in graph-based data mining. One such model is the $s$-club, which is a vertex subset that induces a subgraph of diameter at most $s$. This model has found use in a variety of fields because lo...

The celebrated Motzkin–Straus formulation for the maximum clique problem provides a nontrivial characterization of the clique number of a graph in terms of the maximum value of a nonconvex quadratic function over a standard simplex. It was originally developed as a way of proving Turán’s theorem in graph theory, but was later used to develop compet...

Jose L. Walteros and Austin Buchanan

We study statistical calibration, i.e., adjusting features of a computational model that are not observable or controllable in its associated physical system. We focus on functional calibration, which arises in many manufacturing processes where the unobservable features, called calibration variables, are a function of the input variables. A major...

In the analysis of networks, one often searches for tightly knit clusters. One property of a “good” cluster is a small diameter (say, bounded by k), which leads to the concept of a k-club. In this paper, we propose new path-like and cut-like integer programming formulations for detecting these low-diameter subgraphs. They simplify, generalize, and/...

In the article “A linear‐size zero‐one programming model for the minimum spanning tree problem in planar graphs” (Networks 39(1) (2002), 53‐60), Williams introduced an extended formulation for the spanning tree polytope of a planar graph. This formulation is remarkably small (using only O(n) variables and constraints) and remarkably strong (definin...

This article considers the node‐weighted Steiner tree (NWST) problem and the maximum‐weight connected subgraph (MWCS) problem, which have applications in the design of telecommunication networks and the analysis of biological networks. Exact algorithms with provable worst‐case runtimes are provided. The first algorithm for NWST runs in time for n‐v...

In many network applications, one searches for a connected subset of vertices that exhibits other desirable properties. To this end, this paper studies the connected subgraph polytope of a graph, which is the convex hull of subsets of vertices that induce a connected subgraph. Much of our work is devoted to the study of two nontrivial classes of va...

The vertex cover polytopes of graphs do not admit polynomial-size extended formulations. This motivates the search for polyhedral analogues to approximation algorithms and fixed-parameter tractable (FPT) algorithms. In this paper, we take the FPT approach and study the k-vertex cover polytope (the convex hull of vertex covers of size k). Our main r...

In this article, a heuristic is said to be provably best if, assuming , no other heuristic always finds a better solution (when one exists). This extends the usual notion of “best possible” approximation algorithms to include a larger class of heuristics. We illustrate the idea on several problems that are somewhat stylized versions of real-life ne...

This paper explores techniques for solving the maximum clique and vertex coloring problems on very largescale real-life networks. Because of the size of such networks and the intractability of the considered problems, previously developed exact algorithms may not be directly applicable. The proposed approaches aim to reduce the network instances to...

This paper considers the minimum k -connected d -dominating set problem, which is a fault-tolerant generalization of the minimum connected dominating set ( MCDS) problem. Three integer programming formulations based on vertex cuts are proposed ( depending on whether d < k, d D k, or d > k) and their integer hulls are studied. The separation problem...

A connected dominating set (CDS) is commonly used to model a virtual backbone of a wireless network. To bound the distance that information must travel through the network, we explicitly restrict the diameter of a CDS to be no more than s leading to the concept of a dominating s -club. We prove that for any fixed positive integer s it is NP-complet...

We describe an algorithm for the maximum clique problem that is parameterized by the graph’s degeneracy
$d$
. The algorithm runs in
$O\left( nm+n T_d \right) $
time, where
$T_d$
is the time to solve the maximum clique problem in an arbitrary graph on
$d$
vertices. The best bound as of now is
$T_d=O(2^{d/4})$
by Robson. This shows tha...

## Projects

Projects (2)

Conflict graphs have been proposed to aid in the solution of 0-1 programs. While previous works have used these graphs to generate cuts, we take a different approach based on an extended formulation. We demonstrate that our extended formulation works well in practice when the conflict graph is dense and prove that it has desirable worst-case properties not exhibited by the usual formulations in terms of formulation strength, formulation size, and number of branch-and-bound nodes.

This paper considers the problem of assigning aircraft to gates at an airport. The objective that we consider is to minimize the total distance walked by passengers in the airport terminal. We propose an integer programming (IP) formulation for this problem. It exploits the sparsity of the airport terminal and the properties of interval graphs.